3 years ago

# Electromagnetic decays of the neutral pion investigated in the Dyson-Schwinger formalism.

Richard Williams, Gernot Eichmann, Christian S. Fischer, Esther Weil

We summarize recent work in determining the transition form factor (TFF) of the neutral pion ($\pi^0 \to \gamma^*\gamma^*$), by solving the non-perturbative Dyson-Schwinger and Bethe-Salpeter equations. We first study the transition form factor, followed by the rare decay $\pi^0 \to e^+ e^-$, which requires the TFF as input. In addition to the aspects of truncation required to compute the solution, we discuss unexpected behavior in the large $Q^2$ regime (with $Q^2$ the photon virtuality), and also touch on a path deformation in the complex plane to access the total decay rate for the rare decay.

Publisher URL: http://arxiv.org/abs/1710.08169

DOI: arXiv:1710.08169v2

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